Page 20 - NCERT Books

108 MATHEMATICS

3. Find the square root of the following decimal numbers.
(i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25
(v) 31.36
4. Find the least number which must be subtracted from each of the following numbers
so as to get a perfect square. Also find the square root of the perfect square so
obtained.
(i) 402 (ii) 1989 (iii) 3250 (iv) 825
(v) 4000
5. Find the least number which must be added to each of the following numbers so as
to get a perfect square. Also find the square root of the perfect square so obtained.
(i) 525 (ii) 1750 (iii) 252 (iv) 1825
(v) 6412
6. Find the length of the side of a square whose area is 441 m .
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7. In a right triangle ABC, ∠B = 90°.
(a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB
8. A gardener has 1000 plants. He wants to plant these in such a way that the number
of rows and the number of columns remain same. Find the minimum number of
plants he needs more for this.
9. There are 500 children in a school. For a P.T. drill they have to stand in such a
manner that the number of rows is equal to number of columns. How many children
would be left out in this arrangement.

WHAT HAVE WE DISCUSSED?

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1. If a natural number m can be expressed as n , where n is also a natural number, then m is a
square number.
2. All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

3. Square numbers can only have even number of zeros at the end.
4. Square root is the inverse operation of square.
5. There are two integral square roots of a perfect square number.

Positive square root of a number is denoted by the symbol .

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For example, 3 = 9 gives 9 = 3